Sometimes, something has to give and it might be a screw head. Because it is
a stress failure, the metal gets hard and doesn't respond to drilling or cutting
- plus what's left is too small anyway.

Here's
a headless screw problem in my Twilight Zone. That's the mechanism for
the mini playfield ramp diverter. The head for the right hand mounting
screw is gone, leaving a useless stump. The previos repairer clamped it
in place with a couple of screws on either side.

The first step is to create a relief around the screw thread. I used
a Dremel with a little milling ball attachment. This shape is
convenient, as it digs and widens without going out of control. I simply
ran it around the screw thread as a guide and got this nice circular
pit.

Now,
the screw thread comes out easily with a pair of locking pliers.

There's
the now-empty hole.

I
patched it with marine stick epoxy. I believe this to be stronger than
the wood stick epoxy. It's important to fill the hole and leave no
voids. The bamboo serves as a guide for the screw hole, and provides
something for the threads to bite into. I'll finish up with some wood
coloring once the stuff is hard.